Christ! What's with all the presumptuous posts here? Someone asked me for an example of what I might want to burn to gauge the laser power that I would need and I answered the question with precisely that context in mind: to give you an idea of the power rating of the laser I want (at least). I wasn't actually giving an exhaustive list of everything I wanted to do, just an example of the power I wanted. Mainly I just wanted to learn laser specs (how much X amount of power is supposed to cost and how powerful that rating is).
Not really presumtions, that's statistics, you follow common pattern of those ignorant people with lack of inteligence and/or responsibility to be recommended to get any laser (or trolls, whatever they usually get ban soon). That does not mean you are one of them and I'm not even saying that to make it clear. Just take it easy here, this hobby is very specific as law developement makes it harder to perform for those responsible and missuse of lasers has significant influence on this. So, behaving like one of morons makes you boxed in the moron category. (Really burning ants is not a good example to start with especially as point no. 1. - it is like showing red flag to bull.
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Whatever, I believe you can enjoy lasers, just listen and learn here, noone here will give you bad advice intentionally.
Regarding IR laser - definitely get something visible, you cannot even guess how it will bounce from something or hit something you do not want to burn if you do not see it. With visible laser you can adjust it faster than you burn curtain or something, also there is less likelihood you forget it on and put your glasses off. Seriously start with something of lower power (class 3B), even those cheap blue possible reach 1 W are very bright. Once you will see awesome laser beam of high power, you will likely want to use it to shine around, do some more experiments (laser light is very specific and awesome stuff can be done with it), not only to burn - so here class 3B (like 100 mW green recommended above) is very useful and versatile. To burn paper or cardboard, you will need extreme powers to put them in open fire, however even class 3B might leave a burn mark (especially at top of power limit of class 3B). Problem is with white paper (black marker dot might be needed) and with certain colors (green laser will not burn green paper well, but red will go fast). But if the white paper is not really thick, it can be done - my Evo burns even cigarette paper, when I light my cigarette with it (therefore not just darker tobacco at the open end), with focussing lens there is no problem to engrave cardboard. Also I would not recommend something at the edge of the visible spectre (like 405 nm - violet), these seems to be very dim, but there is a huge power in them. My 500 mW 405 nm looks like stronger pointer, but definitely it puts power of class 4 laser and has incredible burning effects. It is like "mostly invisible" laser. With blue-green (depending on day or night vision adaptation) you get the most visibility, therefore you might recognize it is too bright to watch and be somehow more safe.
Regarding heat generation at distance 2-3 meters - you will likely need some optics (magnifying glass for example) at that place unless you have high powers. Or if you have good beam specs like 100 - 200 mW might be sufficient - my 473 nm laser (you might check my review - link in my signature) is able to light up cigarette even 4 meters far (even it is "low" power - the beam is excelent, so it does not spreads too much and is able to burn far).